ABSTRACT In this paper, we propose a new heuristic strategy to solve linear integer mathematical problems. The strategy begins by finding the optimal solution of the continuous associated problem and the simplex directions from that optimal solution. A total of n − m problems are generated and solved by the strategy, where m is the number of constraints and n is the number of variables of the problem. The best solution to those problems is the solution to the original problem. Several instance problems were randomly generated to validate the strategy, and our strategy finds good solutions in 80% of the instances. We also tested the proposed strategy with instances of the MIPLIB 2017. We compare a total of 39 instances and on average our strategy performed 47% fewer iterations than the solver, in 34 of 39 instances, the strategy found good solutions.

ABSTRACT In this paper, we present the integration of two problems related to the operations in a port terminal: the Berth Allocation Problem (BAP) integrated with the Machine Assignment Problem. We present a mixed-integer linear programming (MILP) formulation, capable of assigning and scheduling incoming vessels to berthing positions and the assignment of machines for handling the vessels. The machines can be quay cranes, mobile cranes, straddle carriers, forklifts, trucks, and any other machine. The problem aims to minimize the waiting time plus the handling time of the vessels. To solve the problem, we developed a heuristic algorithm, capable of solving a problem instance in seconds. To compare the results, we generate several instance problems based on real data and solve them with our MILP formulation implemented in a solver, our heuristic, and a First In First Out (FIFO) algorithm. The solver was able to find solutions only in small-scale instances, and the heuristic was able to find good solutions for all instances.

ABSTRACT Maritime shipping is vital to worldwide commerce. Due to the high flow in ports throughout the world, the efficient allocation of vessels in berths has become a problem. A new mathematical model and several algorithms are proposed in this paper to planning the allocation of the vessels in berths and the allocation of resources to the service of each vessel. Those resources, in general, are machines to load or unload vessels. The mathematical model was implemented on Cplex and can solve small scale instances, due to its high complexity. To solve larger instances, a genetic algorithm-based metaheuristic, a first-in first-out heuristic, and a machine allocation algorithm are also proposed in this paper. The model and the algorithms produce very useful and interesting results. Comparing, the results produced by the GA are, on average, 94% better than the results of the Cplex and 26% better than the results of FIFO.

ABSTRACT The amortization systems, also called as amortization methods, are used to compute the installment value that a client must disburse (or spend) to pay off a loan or financing with the number of installments and the interest rate agreed for the loan or financing. This paper shows that the German Amortization System makes an inconsistent use of the interest paid in advance in its definition and generates an effective interest rate higher than the contracted, which makes this system abusive and unfair to the clients. In this article, two forms of correcting the German Amortization System are also proposed, making the effective interest rate equals to the contractual interest rate.